User blog:XXxKennyDashxXx/A NEW NOTATION! HBAN.
I am working on a new notation called "Hyperbracket Array Notation", or HBAN for short. It starts out almost identical to BEAF, but then shoots out into its own direction! It will become an actual array notation after a while. So, without further ado, here it is! Hyperbracket Array Notation (HBAN) Definition Rule 1: &n = 10^^n Rule 2: &a1c...z = a Rule 3: &abc...z = &a[&ab-1...z]c-1...z That's all for Part 1 of a lot! For an FGH comparison with HBAN and extensions, check out the bottom of the page! HOWEVER, '''there is more! Let's extend this to... Extended Hyperbracket Array Notation (EHBAN) Definition (unstable) From this point on, ''currently rules are not official. Rule 1: &{1}n = &nn...nn with n entries. Rule 2: &{n}m = &{n-1}{n-1}{n-1}...{n-1}{n-1}{n-1}m with m {n-1}s. Rule 3: &{a,b,c...y,z}n = &{a,b,c...&{a,b,c... ...y,z},z-1},z-1}...} with n nests. Rule 4: &{a&b}n = &{a,a,a...a,a,a}n with b entries. Here, it's still the same as BEAF. Also define a &{a,b(1)c}n, and so on to match with the HBAN array of operator variation. Rule 5: &{a&&&...&&&b}n with m &s = &{a&&&...&&&a&&&...&&&a}n with m-1 &s and b & groups. Rule 6: &{a^b}n = &{a&&&...&&&a}n with b &s. Next, define it with the same rules of Extended Cascading-E Notation, up until &{a&^^^...^^^&b}n And that concludes the EHBAN rules. BEAF legions only match up with &{a&&b}n, or the number of single &s. Remember, this notation is a W.I.P. Definitions may be extremely ill at times. Next, we have: Geometrical Hyperbracket Array Notation (GHBAN) Definition (unstable) &{n^^^...^^^n}n with m ^s = {n,m(●)2} Next, there's {n,m(●)3} which is {(n,n(●)2)(●)2)...} with m nests. Continuing, there's {n,n(●)(n,n(●)n,n...)...)} with m nests, which is {n,m(●●)2} Using the Hyper-E rules again, we have: {a,b(●^●)2} = {a,a(●●●...●●●)a} with b ●s. ... Then, {a,a(●^^^...^^^●)a} with b ^s = {a,b(●_2)2} Do the entire process again. {a,a(●_2^^^...^^^●_2)a} with b ^s = {a,b(●_3)2} {a,a(●_{a,a(●_...)a} with b nests = {a,b(♦)2} Do the same process again. Next... {a,a(♦_{a,a(♦_...)a} with b nests = {a,b(▲)2} And so on. That's the end of GHBAN! Next comes... Alphabetical Hyperbracket Array Notation (AHBAN) Definition (unstable) This extension uses Greek letters to diagonalize over lower-class Greek letters! So here's a very informal definition of it! We start with: {a,b(Ξ)2} = {a,a(b-th symbol)a} where the sequence of symbols is {●,♦,▲...} It's easy to remember after the first two, because it's also the number of sides that the symbol has. After the triangle, it would be a sqaure, and then a pentagon, and so on. Examples: {3,1(Ξ)2} = {3,3(●)3} {3,2(Ξ)2} = (3,3(♦)3} {3,10(Ξ)2} = {3,3(some kind of filled-in decagon)3} Do the same thing until... {a,a(Ξ^^^...^^^Ξ)a} which would be {a,a(Ξ_2)a}. Next, {a,a(Ξ_...a)a} with b subscript nests = {a,b(Ξ●)2} It's just like the sequence: circle, diamond, triangle, square, etc., except with a Xi at the beginning! Now since Xi = sup{circle, diamond, triangle, square, pentagon...}, we could have Xi Xi = sup{Xi circle, Xi diamond, Xi triangle...} Then Xi Xi Xi! {a,b(Ξ^Ξ)c} {a,a(Ξ^^^...^^^Ξ)a} with b ^s = {a,b(Ψ)2} {a,b(Ψ^^^...^^^Ψ)c} with b ^s = {a,b(some kind of third greek letter)2} Now, just like in FGH, we need some way to diagonalize over things, but instead of the ordinals epsilon, zeta, eta, etc., we have Xi, Psi, etc. That's featured multiple times in... Extended Alphabetical Hyperbracket Array Notation (EAHBAN) Definition (unstable) Now, here's the diagonalization I was talking about. Define β = sup{Ξ,Ψ...} So... {3,1(β)2} = {3,3(Ξ)3} {3,2(β)2} = {3,3(Ψ)3} And so on! Next, you can have (just like before): {a,b(β●)c} Then, since Ξ = sup{circle, diamond, triangle...}, we could have: {a,b(βΞ)c} And then: {a,b(βΨ)c} And then, just like we did with Xi... {a,b(ββ)c} as the sequence of {a,b(beta xi)c}, {a,b(beta psi)c}... {a,a(β^^^...^^^β)a} b ^s = {a,b(α)2} Now, we can define another sequence, as Λ. Λ = sup{beta, alpha...} So Λ is a sequence of sequences! Next, you could use Rho (P)! {a,a(lambda^^^...^^^lambda)a} with b ^s = {a,b(P)2} Next, define Υ (upsilon) as the sequence: sup{lambda, rho...} It's a sequence of (sequences of sequences)!!!!! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAARRRRGHHHHHH!!!!! Now, we could make a sequence of sequences of sequences of sequences... but we need to acelerate faster... with: Alpha-Sequence Hyperbracket Array Notation (ASHBAN) Definition (unstable) Confused yet? Let's define Δ (delta) as: sup{sequence of letters, sequence of sequences of letters, sequence of sequences of sequences of letters...} or sup{beta, lambda, upsilon...} A sequence of sequences is a super sequence. A sequence of sequences of sequences is a duper sequence A sequence... ... So, a sequence of the number of nests is a hyper sequence. (delta) A sequence of deltas is a super hyper sequence. A sequence of those ^^^^^ is a duper hyper sequence. A sequence of all of the above is a hyper sequence. A sequence of all of the above, now, is a dyper sequence. Tryper sequence. Hard to picture? Go to the contents list and skip to the bottom with the numbers! But anyway... Eta (H) = sup{hyper, dyper, tryper...} So Eta is an ultra sequence. Next, do the same thing. Epsilon (ε) = uber sequence. Super = 1st adjective used Hyper = 2nd adjective used Ultra = 3rd adjective used Uber = 4th adjective used Omega (Ω) = sup{super,hyper,ultra,uber} I know this sounds stupid. The limit of ASHBAN is &{n,n(Ω^^^...^^^Ω)n} with n ^s. I'm not sure about FGH. Numbers Defined By Me With HBAN (for fun I guess) Okay, here they are! Don't ask where I get the names from. Fine, random word generator, I pick the ones that sound really cool. Then I add things like bi- tri- and others. *&100 = Nanoarrow The wee, '''''wee number here is exactly equal to a giggol. *&[&100] = Microarrow (10^^10^^100) *&[&[&100]] = Milliarrow (10^^10^^10^^100) *&1001 = Fluffster ~ 10^^^100 (because it's so small that it's cute) *&1002 = Duffster ~ 10^^^^100 *&100100 = Skizzlespeck ~ {10,100,102} *&10011 = Skizzlecrumb ~ {10,100,1,2} *&10021 = Skizzblespeck *&10031 = Skizztrlespeck *&1001001 = Skizzgospeck *&10012 = Skizzledeck *&10022 = Skizzbledeck *&10032 = Skizztrledeck *&1001002 = Skizzgodeck *&1001003 = Skizzgotrek *&100100100 = Trizzlespeck *&100100100100 = Quizzlespeck *&100100100100100 = Quintizzlespeck *&{1}100 or &100100...100100 with 100 100's. = Alerrawia *&{1}100100 = Alerrabia *&{1}100100100 = Alerratria *&{1}{1}100 = Dalerrawia *&{1}{1}{1}100 = Tralerrawia *&{2}100 = Deutero-alerawia *&{2}{2}100 = Deutero-dalerrawia *&{3}100 = Trito-alerawia *&{4}100 = Teterto-alerawia *&{100}100 = Go-alerawia *Replace the following "Templates" with double braces around 1, 2, 3, and 100, and then triple braces around 1, 2, 100, and quadruple braces around 100. Sorry about that. *& 100 or &{&{...&{100}...}}}100 with 100 nests = Ubooxa *& 100 = Dubooxa *& 100 = Trubooxa *& 100 = Gobooxa *& }100 = Trooxa *& }100 = Dutrooxa *& }100 = Gotrooxa *&{}100 = Goquooxa *&{100,100}100 or &{...{100}...}100 with 100 braces = Spalkorealm *&{100,100,100}100 = Tralkorealm *&{100&100}100 = Golkorealm *&{100^100&100}100 or a so-called "&{100,100(100)2}100" = Dimendorealm *&{100&100&100}100 = Triloqerratra *&{100&&100}100 = Duberratra *&{100&&&100}100 = Dutrerratra *Credit to Sbiis Saibian's ULNL Part 3 for some of the proceeding numbers. *&{100&^&100}100 = Godgamperex *&{100&^&&100}100 = Gridgamperex *&{100&^&&&100}100 = Kubigamperex *&{100&^&^&100}100 = Thorgamperex *&{100&^&^&^&100}100 = Totholgamperex *&{100&^^&100}100 = Tethragamperex *&{100&^^^&100}100 = Pentacthugamperex *&{100&^^^^&100}100 = Hexacthugamperex *&{100,100(●)2} or &{100&^^^...^^^&100}100 with 100 ^s. = Dolgogox *&{100,100(●)3} = Trolgogox *&{100,100(●)4} = Quolgogox *&{100,100(●)100} = Goxlogox *&{100,100(●●)100} = Goxlogoxx *&{100,100(●●●)100} = Goxlogoxxx *Don't ask. And don't try to pronounce these all at once. *&{100,100(●^●)100} = Godgogox *&{100,100(●^^●)100} = Tethrogogox *&{100,100(●^^^●)100} = Pentacthugogox *&{100,100(●_2)100} = Goxlodox *&{100,100(●_3)100} = Goxlotrox *&{100,100(●_100)100} = Goxloxox *&{100,100(♦)100} = Diamoqibehemoth *&{100,100(▲)100} = Triangoqibehemoth *UNDER CONSTRUCTION! Other names that may be used: Exteria Extreovlok Grodsaar Drirathiel Qakkqal Sirooxrul Thynolspoth Gaqemnern Spoloqooxslot Yqasblap Gikglozoox Phliirkex Oeiwlax Phloxxodene (sounds like a drug, lol!) Ixgitflyefgogologog Adding more soon! :) Category:Blog posts